How does regulating doctors’ admissions affect health expenditures? Evidence from Switzerland

Background Cost containment is a major issue for health policy, in many countries. Policymakers have used various measures to deal with this problem. In Switzerland, the national parliament and subnational (cantonal) governments have used moratoriums to limit the admission of specialist doctors and general practitioners. Methods We analyze the impact of these regulations on the number of doctors billing in free practice and on the health costs created by medical practice based on records from the data pool of Swiss health insurers (SASIS) from 2007 to 2018 using interrupted time series and difference-in-differences models. Results We demonstrate that the removal of the national moratorium in 2012 increased the number of doctors, but did not augment significantly the direct health costs produced by independent doctors. Furthermore, the reintroduction of regulations at the cantonal level in 2013 and 2014 decreased the number of doctors billing in free practice but, again, did not affect direct health costs. Conclusions Our findings suggest that regulating healthcare supply through a moratorium on doctors’ admissions does not directly contribute to limiting the increase in health expenditures. Supplementary Information The online version contains supplementary material available at (10.1186/s12913-022-07735-7).


Supplementary materials
This section presents supplementary materials with additional information on our analysis.
A. Comments on the available data Original data are gathered by matching the ZSR doctor identifiers with the amounts invoiced to health insurers in each month and each canton by specialty as registered in the SASIS data pool. Therefore, this database offers an accurate estimation of the number of doctors billing in free practice by specialty established within one canton and of the related health costs. The available data contain the counts of unique doctor identifiers in each month and in each canton by specialty. The entry reporting the location refers to the canton of work, or, more precisely to the canton where the invoice has been issued. Further, the month of a record represents the month of invoice issuance. Doctors billing services in different cantons have a different ZSR in each canton. Also, one ZSR may bill services in different specialties. Overall, we cannot sum up the cantonal (specialty) counters for the whole Switzerland as we cannot control for duplicate individual doctors among cantons (specialties). Therefore, we only present aggregate figures for the health costs on the level of the whole country (sum of costs from all cantons) but not for the number of doctors (the sum of the cantonal counters would overestimate the true headcount).
C. Regression results for the removal of the national moratorium for GP In Table 3 we report our analysis of the removal of the moratorium for GP. The "Month"-coefficient is not always statistically significant meaning an unclear picture regarding the overall growth rate of the number of GP billing in free practice. Additionally, only in few cantons the removal and the interaction term are relevant.
The interaction term has a significant positive effect in six cantons, concerning essentially border cantons (GE, LU, JU, SG, TG, TI, and SZ) and cantons with large hospitals (BE, GE). This observation could hint that the moratorium removal influenced the immigration of GP into Switzerland from neighboring countries.
In the right-hand side of Table 3, we report the results estimating the effect on the GP health costs. Apart from the intercept, in most cantons no other coefficient is statistically significant. In particular, the time variable ("Month") demonstrates that health costs remained stable during the whole observation period. Only in NE, TI, and ZH, we find a significantly positive interaction term coefficient. Thus, observations for GP are mostly aligned with findings from SP ( Table ??), indicating that the moratorium removal (alone) did not increase further health expenditures.

D. Reintroduction of cantonal moratoriums for SP
In addition to the results presented in the main text of the article, the representation in Figure 2(a) illustrates that, for GE, before the moratorium reintroduction, a yearly growth of 8.11% in the number of doctors billing in free practice is observed. After the reintroduction, this rate was reduced to 1.56%. In Figure 2(b), the lower slope for costs in GE is not statistically significant (see Table 3 in the main article).

E. Regression results for SP health costs by specialty
In Table 4, we present the regression results for SP health costs by specialty for both the removal and reintroduction of the moratorium. We only report results for Note: Results for the moratorium removal are based on 78 months including 60 months before (01/2007-12/2011) and 18 months after (01/2012-06/2013) the removal of the moratorium for SP, see Figure 1 in the main document. Results for the moratorium reintroduction are based on 84 months from 01/2012 to 12/2018 including the canton-specific reintroduction dates. The results concerning the reintroduction of cantonal moratoriums are based on data from the 18 relevant cantons only. The displayed values for the coefficients for "Month", "Rem." and "Month × Rem." respectively "Reint." and "Month × Reint." are multiplied by 10. Values account for the seasonal effect. Significance levels are indicated as follows: * p < 0.1, ** p < 0.05, *** p < 0.01. Table 4 Regression results for health costs by specialty for the SP national moratorium removal in January 2012 and the SP moratorium reintroduction in 18 cantons.
specialties where on average at least 100 doctors have billed medical services in each month. While the analysis on the removal of the national moratorium uses health costs from all 26 cantons, the study on the reintroduction of cantonal moratoriums only considers the costs from the 18 cantons that have reintroduced the regulation.
On the one hand, our results show that removing the moratorium augmented the costs increase from some specialists, such as allergology and clinical immunology, endocrinology and diabetology, and radiology. On the other hand, the reintroduction of the moratorium reduced the costs from these same specialities as well as from other disciplines. Nevertheless, regarding some specialities, such as pathology and pneumology, costs increased after re-introduction of the moratorium. Overall, we cannot confirm a strong cause-effect relationship of the moratorium policies and the increase in health costs, also because in many specialties particular effects that we do not control for may have a more important impact.

F. Regression results for SP per cantonal population
In the following, we discuss the regression results for SP health costs and for the number of SP billing in free practice when divided by the monthly cantonal population. In Table 5, we present the results for SP health costs divided by the monthly cantonal population on the same period for both the removal and reintroduction of the moratorium. As a robustness test of the results presented in the paper, we highlight here that using the SP heath costs divided by the monthly cantonal population has no significant effect on the results compared to the findings presented in Tables 1 and 2. Our results show that the health costs in most cantons were not affected by the moratorium removal even when accounting for the population size. We come to the same conclusion when considering the moratorium reintroduction effect on the health costs per capita.  The displayed values for the coefficients for "Month", "Rem." and "Month × Rem." respectively "Reint." and "Month × Reint." are multiplied by 10. Values account for the seasonal effect. Significance levels are indicated as follows: * p < 0.1, ** p < 0.05, *** p < 0.01. Table 5 Regression results for health costs by cantons for the SP national moratorium removal in January 2012 and the SP moratorium reintroduction in 18 cantons.
Similarly, in Table 6, we present the regression results for the number of SP billing in free practice divided by the monthly cantonal population on the same period for both the removal and reintroduction of the moratorium. Let us also mention that the model specification has been changed since, after division, the outcome variable is no more a counting process that can be modeled by a negative binomial distribution. We modified the previous outcome variable (number of doctors) into a ratio. We ran the model selection procedure again and found that, among the tested models, the Gaussian specification has the lowest AIC. Further, as seen in the table, coefficient values become small. In this case, our results show that the number of SP billing in free practice costs in most cantons were affected by the moratorium removal even when accounting for the population size. We come to the same conclusion when considering the moratorium reintroduction effect on the number of SP per capita. Such results are coherent with what we observe when solely focusing on the number of SP.   Table 6 Regression results for the number of SP billing in free practice for the SP national moratorium removal in January 2012 and the SP moratorium reintroduction in 18 cantons.
G. Difference-in-differences model for the reintroduction of the national moratorium for SP health costs In the following, we use a difference-in-differences (DID) model for the reintroduction of the national moratorium for SP health costs. The theoretical foundation of this methodology is well documented and can be found in, e.g., [1]. In our approach, we estimate two distinct DID models that we distinguish by a divergence in treatment groups. First, in the model "DID (1)", our treatment group is composed of the cantons that reintroduced the moratorium while our control group consists of cantons that did not reintroduce the moratorium. Second, in the model "DID (2)", the treatment group only accounts for cantons having reintroduced the moratorium in 07/2013 while the control group remains unchanged. In doing so, the second approach allows for having a balanced analysis. The following equation describes both models: where the variables C t , Month t and ǫ t are as defined in Section 2.2. The variables CReint t is a binary indicator taking the value of 1 for cantons having reintroduced the moratorium (treatment group) and 0 otherwise (control group). Further, the variable Month t × CReint t represents the interaction effect and is the key measure for evaluating the effect of the moratorium reintroduction on the SP health costs. In our model selection process, we compare this model to similar DID models that include a higher order polynomial form. More precisely, we have compared the AIC values of the presented model (1) with a model adding the quadratic form of the time variable (Month 2 t ) and a model adding both its quadratic and cubic forms (i.e. Month 2 t and Month 3 t ). These models have reported AIC values of 7 401, 7 401 and 7 402, respectively, therefore not showing any model improvement. Further, we come to the same conclusion when comparing BIC values. Based on this analysis and the fact that coefficient values and significance levels are quasi identical, we decided to remain with the linear form. We present the results in Table 7. (1) 15.420 *** .004 * .237 * −.000 DID (2) 15.449 *** .004 * −.275 * .000 Note: The notation "DID (1)" refers to a DID model performed on the overall set of cantons while "DID (2)" identifies a balanced DID model where, in the treatment group, solely the cantons having reintroduced the moratorium in 07/2013 are considered. Table 7 Difference-in-differences (DID) model results for health costs for the SP national moratorium reintroduction.
As a key result, we observe that the variable Month × CReint is not significant, neither in the "DID (1)" nor in the "DID (2)" model. This confirms the absence of an effect of the moratorium reintroduction on health costs. Further, we have performed the DID on the cantons with at least 150'000 inhabitants (BE, GE, ZH, VD and AG) where small sample effects can be excluded. The results are presented in Table 8.

H. Confidence intervals
In the following, we present the confidence intervals for the regression results presented in the main corpus of the manuscript. This will benefit to the present analysis since it will give some indication whether observed null-effects are stemming from real null-effects or simply from small sample size, i.e. lack of power. In Tables 9 and 10, we present the confidence intervals for the regression results presented in Table 1 and Table 3 in the main document, respectively. For the moratorium removal, the confidence intervals for the number of SP interaction terms (Month × Rem.) exclude, in most cases, the null-effect. The opposite is observed with the health costs from SP. When considering the moratorium reintroduction, we still observe that most of the interaction terms' confidence intervals exclude the null effect for the number of SP. Again, the opposite is observed for the health costs from SP. These results reflect the conclusions obtained when using p-values.  Figure 1, main document. The notations "Lower" and "Upper" refer to the lower and upper bounds of the 95%-confidence interval Table 9 Confidence intervals for the regression results presented in Table 1 in the main document. Note: Results are based on 84 months from 01/2012 to 12/2018 including the canton-specific reintroduction dates of the moratorium for SP, see Figure ??. The notations "Lower" and "Upper" refer to the lower and upper bounds of the 95%-confidence interval. Table 10 Confidence intervals for the regression results presented in Table 3, main document.

I. Supplementary analyses and validation tests
In the following, we provide a set of statistical diagnostics to measure the validity and performance of our models. First, we discuss the goodness-of-fit by comparing AIC values between applicable models and by analyzing model residuals. Second, we provide rationales for the interrupted time series linearity assumption. Third, we present the results of a falsification test, which we implemented on the period prior the moratorium removal. Fourth, for the moratorium reintroduction, we apply our model to a control group and compare the results with the treatment group. Finally, we present out-of-sample predictions based on the data prior moratorium removal and compare them with our model prediction.
Goodness-of-fit: In Table 11, we present the AIC values when fitting the observed data for the response variables measuring the number of doctors billing in free practice N t and health costs from doctors C t to selected distributions. Considering the relevant observation periods for the removal and reintroduction of the moratorium (01/2007-06/2013 and 01/2012-12/2018), we separately assess the case of SP and GP. For the number of doctors billing in free practice, we report the goodness-of-fit on the negative binomial and Poisson distributions, while we present results for log-normal and Weibull distributions fitted on the health costs. In our procedure, we have also considered the binomial and geometric distributions for N t and the exponential, normal and Gamma distributions for C t . In all cases, we find that the negative binomial distribution best fits the number of doctors in terms of AIC, while the log-normal distribution outperforms the Weibull distribution and is best suited for health costs.
The analysis of residuals is a relevant statistical tool for evaluating the goodnessof-fit of the interrupted time series model [2]. This method consists in identifying structure, i.e., patterns, in the model residuals. The presence of a pattern is a strong signal for a potential model misspecification or a missing variable. In other words, it indicates that part of the dependent variable behavior is captured by the model error and thus remains unexplained. In contrast, when no structure is observed, we can be confident on the model specification and can reasonably assume that no fundamental covariates are missing in the model. In Figure 3, we present the residuals for the number of and health costs from SP around the removal of the moratorium in GE and ZH. For the presented figures, visual inspection confirms that no clear pattern is observed.
Linearity assumption: In the case of an interrupted time series model, the most important assumption to satisfy is the linearity assumption [3]. When a linear trend exists, it becomes straightforward to isolate the intervention and predict the counter factual. As recommended by [4], we verify such assumption by visual inspection of the data and of the residuals, i.e., as provided above. In Figure 4, we present the raw data for the number of SP and the health costs from SP for GE and ZH.

Removal of the national moratorium
Reintroduction of moratoriums Note: The observation period for study of the removal of the national moratorium is from 01/2007 to 06/2013 for SP and GP. The reintroduction of cantonal moratoriums only concerns SP and is studied on the period from 01/2012 to 12/2018. The columns "Nt" and "Ct" refer to the number of and the health costs from SP respectively GP. The abbreviations "NB" and "P" mean model fits with a negative binomial respectively a Poisson distribution while "LN" and "W" denote fits with a log-normal and a Weibull distribution respectively. "n.a." stands for not applicable. In fact, in the canton ZH, no moratorium has been reintroduced, see Figure 1, main document. number of SP and health costs from SP. Further, we remark that the linear trend post-moratorium removal deviates significantly to the linear trend pre-moratorium removal when focusing on the number of SP. This is less the case for the health costs from SP. Finally, let us mention that the methodology applied, and our conclusion on the applicability of interrupted time series model, are identical to Figure 3 in [4].
Falsification test: In the following, we apply the falsification test to verify alternative dates on the model applied for the removal of the national moratorium for SP. In particular, this approach allows us to measure if changes in slope are related to the intervention or could be observed also at other dates [5]. For this purpose, we select the alternative dates 06/2008 and 06/2010 since both ensure having enough data points before and after the hypothetical intervention. In Table 13     GE, VD and ZH). For both alternative dates, we observe that the coefficients for the moratorium removal ("Rem.") and for the interaction term ("Month × Rem.") are not statistically significant. As expected, results from this falsification test contrast with the significant factors found in Table 1  Note: Results are based on 60 months, i.e. accounting only for the 60 months before the removal of the moratorium for SP(01/2007-12/2011), see Figure 1, main document. The displayed values for the coefficients for "Month", "Rem." and "Month × Rem." are multiplied by 10. Values account for the seasonal effect. Significance levels are indicated as follows: * p < 0.1, ** p < 0.05, *** p < 0.01. Table 13 Alternative dates test for the SP national moratorium removal in January 2012.
Control group: To disentangle the effect of policy under study from any other policy change or any other unobservable factor affecting the outcome variable over time, we tested our model on the control group composed by the cantons having not experienced a moratorium reintroduction (i.e. AG, AI, AR, FR, GR, JU, ZG and ZH). Such analysis is possible only for the moratorium reintroduction since, for the moratorium removal, the political intervention has been effective in all cantons. In Table 14, we present the results for the moratorium reintroduction for the cantons having not experienced reintroduction. As for the results on the treatment group (cf. Out-of-sample test: The out-of-sample test is a powerful tool to assess the forecasting accuracy of a model [6]. In our setup, we use this approach to compare whether our model results (model) post moratorium removal diverge from the forecast on the same period (out-of-sample) obtained from fitting the model only on the 60 months prior intervention. In doing so, we bring further evidence for the results presented in the main part of the manuscript that rely on p-values. In Figure 6, we present the model and the out-of-sample predictions for the number of and health costs from SP for the moratorium removal in GE and ZH. Considering the number of SP in GE and ZH in the period post moratorium removal, we note that the confidence intervals of the model predictions diverge from the ones of the out-of-sample predictions. This confirms that the removal has led to a significant increase in the number of SP. We conclude the opposite when focusing on the health costs from SP in GE and ZH since the confidence intervals of the model and the out-of-sample predictions intersect on the post-intervention period. In each graph, the plain curve reports the fit of the regression model and two dashed curves indicate the 95%-confidence interval. The grey curve reports the out-of-sample prediction obtained from fitting the regression model on the period from 01/07 to 12/11. A vertical dashed line indicates the last date before the removal of the moratorium. Finally, Tables 18 and 19 present the p-values for the policy intervention and the interaction effect coefficients for both the moratorium removal and reintroduction when using the Bonferroni method. In doing so, we account for multiple testing. Results are only reported for the intervention and interaction variables. The results after correction are similar to the original ones (cf. Tables 1 and 3)